Chapter 2: Statically Indeterminate - Union...

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 1

Chapter 2:Statically Indeterminate

DefinitionApproach

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 2

Statically Indeterminate Problems

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ESC023: Mechanics of Materials 3

Rules to Solve ProblemsMethod of Superposition

Decompose the statically indeterminate problem into two (or more statically determinate problems.Assumptions

The loading must be linearly related to the stress or displacement that is to be determinedThe loading must not significantly change the original geometry of the configuration or configuration of the member

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 4

Superposition MethodProcedure

Relieve the redundant constraint in the structureDetermine this structures static reactionRemove all external applied loads on the original structure and apply the redundant constraint as a pseudo-force.The solution of the original problem is arrived at by superimposing the solution from the preceding two parts through a constraint Equation

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 5

Relieve Redundant Constraint

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ESC023: Mechanics of Materials 6

Determine Static Reaction

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ESC023: Mechanics of Materials 7

Introduction of Pseudo-Force

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ESC023: Mechanics of Materials 8

Combine Solutions with Constraint Equation

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ESC023: Mechanics of Materials 9

Example 1Consider a steel rod that has a diameter of 5mm. It is attached to a fixed wall at A, and before it is loaded there is a gap between the wall at B’ and the rod of 1mm. Determine the reaction at A and B’ if the rod is subject to an axial force of P=20kN as shown. Neglect the size of the collar at C. E=200 GPa

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 10

Example 2The ends of the 15mm diameter steel rods “BE”and “CD” are single threaded with a pitch of 2.25mm. Knowing that after being snugly fitted, the nut at C is tightened one full turn, determine (a) the tension in rod “CD”, (b) the deflection of point “C”of the rigid member “ABC”. The elastic modulus of steel is 200GPa.

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 11

Kinematic Constraint

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 12

Implication of tightening the nut one more turn.